Question: Simplify the following expression: $\dfrac{121a^3}{99a}$ You can assume $a \neq 0$.
Answer: $ \dfrac{121a^3}{99a} = \dfrac{121}{99} \cdot \dfrac{a^3}{a} $ To simplify $\frac{121}{99}$ , find the greatest common factor (GCD) of $121$ and $99$ $121 = 11 \cdot 11$ $99 = 3 \cdot 3 \cdot 11$ $ \mbox{GCD}(121, 99) = 11 $ $ \dfrac{121}{99} \cdot \dfrac{a^3}{a} = \dfrac{11 \cdot 11}{11 \cdot 9} \cdot \dfrac{a^3}{a} $ $\phantom{ \dfrac{121}{99} \cdot \dfrac{3}{1}} = \dfrac{11}{9} \cdot \dfrac{a^3}{a} $ $ \dfrac{a^3}{a} = \dfrac{a \cdot a \cdot a}{a} = a^2 $ $ \dfrac{11}{9} \cdot a^2 = \dfrac{11a^2}{9} $